A cereal box has dimensions of 10 1/2 inches by 7 1/2 inches by 2 1/2 inches. What is the volume of the cereal box? 19 1/2 in³ 2
1 answer:
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Answer:
Area of ΔPQR is 28 units²
Step-by-step explanation:
-P is the point with coordinates ( 0, y-intercept for line x-2y+2 =0)
-rearrange the equation in the point-slope form y=mx+b to find the y coordinate of the point P( 0, b)
x-2y+2 = 0, subtract x and 2 from both sides
-2y = -x-2, divide by -2 both sides
y= (1/2)x +1 so b=1 and P (0, 1)
-Q is the point with coordinates ( 0, y-intercept for line 3x+y -15 =0)
-rearrange the equation in the point-slope form y=mx+b to find the y coordinate of the point Q( 0, b)
3x +y -15 =0, subtract 3x and add 15 to both sides
y= -3x +15 so b=15 and Q(0,15)
-R is the intersection of the two lines so is the solution of the system of equations y= (1/2)x +1 and y= -3x +15
(1/2)x +1 = -3x +15, add 3x and subtract1
(1/2) x+3x = 15-1, combine like terms
(7/2)x = 14 , multiply both sides by 2
7x = 28, divide both sides by 7
x= 4
y= (1/2)x +1 = (4/2) +1 =3 so R(4,3)
- the area of ΔPQR is (base *height)/2
base= 15-1= 14
height = 4
A= (14*4)/2 = 14*2 = 28
Answer:
= 4√53 units
that is option(a)
Step-by-step explanation:
all sides of the square are of the same length
so if we get the length if this side, we can calculate its perimeter
there's this formula,
<u>side length between two points, let's say A(x, y) and B(p, q), is equal to </u>
so here we go,
the same points A and B here are
(4, 7) and (-3, 5)
therefore, side length :-
the side length comes out to be <u>√(</u><u>53</u><u>) </u>
now perimeter of a square is
4 × side length
= 4√53 units